scipy.special.roots_sh_chebyu¶
-
scipy.special.
roots_sh_chebyu
(n, mu=False)[source]¶ Gauss-Chebyshev (second kind, shifted) quadrature.
Computes the sample points and weights for Gauss-Chebyshev quadrature. The sample points are the roots of the n-th degree shifted Chebyshev polynomial of the second kind, \(U_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([0, 1]\) with weight function \(f(x) = \sqrt{x - x^2}\).
- Parameters
- nint
quadrature order
- mubool, optional
If True, return the sum of the weights, optional.
- Returns
- xndarray
Sample points
- wndarray
Weights
- mufloat
Sum of the weights